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3 years ago

Factor each trinomial. Then match the polynomial (term) on the left with its factored form (definition) on the right.

1 answer:

4 0

X^2 - 4x - 12 = x^2 + 2x - 6x - 12 = x(x + 2) - 6(x + 2) = (x - 6)(x + 2)
x^2 + 4x - 12 = x^2 - 2x + 6x - 12 = x(x - 2) + 6(x - 2) = (x - 2)(x + 6)
x^2 - x - 12 = x^2 + 3x - 4x - 12 = x(x + 3) - 4(x + 3) = (x - 4)(x + 3)
x^2 - 7x - 12 is prime.

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X + y = 7, what is the value of 2x + 2y -2? btw please hurry, thx <3

stira [4]

Answer:

The answer is 12 because 2x is just 8 and 2y is just 6 so add that and get 14 then subtract 2.

Step-by-step explanation:

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2 years ago

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svetoff [14.1K]

Answer:

a = - $\frac{9}{2}$ , b = - $\frac{25}{4}$

Step-by-step explanation:

To obtain the required form use the method of completing the square

add/ subtract ( half the coefficient of the x- term)² to x² - 9x

y = x² + 2(- $\frac{9}{2}$ )x + $\frac{81}{4}$ - $\frac{81}{4}$ + 14

= (x - $\frac{9}{2}$ )² - $\frac{81}{4}$ + $\frac{56}{4}$

= (x - $\frac{9}{2}$ )²- $\frac{25}{4}$ ← in the form (x + a)² + b

with a = - $\frac{9}{2}$ and b = - $\frac{25}{4}$

8 0

3 years ago

Read 2 more answers

The owner of a clothing store borrows $5,000 for 1 year at 14.5% interest. If he pays the loan back at the end of the year, how

oksano4ka [1.4K]

Answer:

Depends on the sort of interest, He could have paid annual interest, compound interest, monthly. If it is annual interest the answer is 5,725$

Step-by-step explanation:

Multiply the initial value by the growth (1.145)

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3 years ago

Please help me on this question, I was struggling with it for an hour from now.

krek1111 [17]

Answer:

Step-by-step explanation:

P(3) = ⅙

P(5) = ⅙

Trials are independent so,

P(3 then 5) = 1/6 × 1/6 = 1/36

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3 years ago

4. A small high school holds its graduation ceremony in the gym. Because of seating constraints, students are limited to a maxim

Ad libitum [116K]

Answer:

(a) The mean and standard deviation of X is 2.6 and 1.2 respectively.

(b) The mean and standard deviation of T are 390 and 180 respectively.

(c) The distribution of T is N (390, 180²). The probability that all students’ requests can be accommodated is 0.7291.

Step-by-step explanation:

(a)

The random variable X is defined as the number of tickets requested by a randomly selected graduating student.

The probability distribution of the number of tickets wanted by the students for the graduation ceremony is as follows:

X P (X)

0 0.05

1 0.15

2 0.25

3 0.25

4 0.30

The formula to compute the mean is:

$\mu=\sum x\cdot P(X)$

Compute the mean number of tickets requested by a student as follows:

$\mu=\sum x\cdot P(X)\\=(0\times 0.05)+(1\times 0.15)+(2\times 0.25)+(3\times 0.25)+(4\times 0.30)\\=2.6$

The formula of standard deviation of the number of tickets requested by a student as follows:

$\sigma=\sqrt{E(X^{2})-\mu^{2}}$

Compute the standard deviation as follows:

$\sigma=\sqrt{E(X^{2})-\mu^{2}}\\=\sqrt{[(0^{2}\times 0.05)+(1^{2}\times 0.15)+(2^{2}\times 0.25)+(3^{2}\times 0.25)+(4^{2}\times 0.30)]-(2.6)^{2}}\\=\sqrt{1.44}\\=1.2$

Thus, the mean and standard deviation of X is 2.6 and 1.2 respectively.

(b)

The random variable T is defined as the total number of tickets requested by the 150 students graduating this year.

That is, T = 150 X

Compute the mean of T as follows:

$\mu=E(T)\\=E(150\cdot X)\\=150\times E(X)\\=150\times 2.6\\=390$

Compute the standard deviation of T as follows:

$\sigma=SD(T)\\=SD(150\cdot X)\\=\sqrt{V(150\cdot X)}\\=\sqrt{150^{2}}\times SD(X)\\=150\times 1.2\\=180$

Thus, the mean and standard deviation of T are 390 and 180 respectively.

(c)

The maximum number of seats at the gym is, 500.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.

Here T = total number of seats requested.

Then, the mean of the distribution of the sum of values of X is given by,

$\mu_{T}=n\times \mu_{X}=390$

And the standard deviation of the distribution of the sum of values of X is given by,

$\sigma_{T}=n\times \sigma_{X}=180$

So, the distribution of T is N (390, 180²).

Compute the probability that all students’ requests can be accommodated, i.e. less than 500 seats were requested as follows:

$P(T$

Thus, the probability that all students’ requests can be accommodated is 0.7291.

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3 years ago